A circle has a radius of $3$. An arc in this circle has a central angle of $345^\circ$. What is the length of the arc? ${6\pi}$ ${345^\circ}$ $\color{#DF0030}{\dfrac{23}{4}\pi}$ ${3}$
Answer: First, calculate the circumference of the circle. $c = 2\pi r = 2\pi (3) = 6\pi$ The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{360^\circ} = \dfrac{s}{c}$ $\dfrac{345^\circ}{360^\circ} = \dfrac{s}{6\pi}$ $\dfrac{23}{24} = \dfrac{s}{6\pi}$ $\dfrac{23}{24} \times 6\pi = s$ $\dfrac{23}{4}\pi = s$